Sujet: Question
Nom: rachel
Qui êtes-vous? étudiant

a particle is moving along the curve whose equation is:
(xy^3)/(1+y^2)=8/5
assume the x-coordinate is increasing at the rate of 6 units per second when
the particle is at the point (1,2).
a. at what rate is the y-coordinate of the point changing at that instant?
b. is the particle rising or falling at that instant?

Hi Rachel,

I would first multiply both sides of the expression by 5(1 + y²) to get

5xy³ = 8(1 + y²)

At this point the problem is very similar to the question you sent a couple of days ago. As in that problem you need to see the variables, here x and y, as functions of time t. As the particle moves along the curve both x and y change.

You are told that when the particle is at (1,2) the x-coordinate is increasing at the rate of 6 units per second. That means that when x = 1 and y = 2 you know that dx/dt = 6 units per second. You are asked to find dy/dt at that instant.

As in your previous problem you need to differentiate both sides of the equation with respect to t. This will give you an equation involving x, y, dx/dt and dy/dt. Since you know x, y and dx/dt at the instant in question you can find dy/dt.

Penny